Cold weather does not and cannot affect your WiFi connection.
However when it's cold outside the ground can shift and crack and lead to damaged cables that carry your internet signal from your house to wherever it leads to.
The cold weather causes the ground to heave as it freezes, potentially damaging cable lines.
Also in the cold weather more people are online streaming videos, watching Youtube, downloading files, browsing the internet etc.
That extra internet traffic can slow down your internet connection because when more people are using the internet the slower the traffic for the internet can get through.
Cloudy conditions have been shown to cause spotty WiFi signals and even rain but cold weather cannot effect your WiFi directly.